Abstract

The relationship between the stiffness properties of actuators configured in an agonist-antagonist configuration and the stiffness of the joint is simple but not intuitively obvious. In this paper, this relationship is investigated and it is shown that the stiffness properties (hardening or softening) of the joint depend on the second derivative of the individual actuator stiffness with respect to actuator displacement. Numerical examples are given to illustrate the relationship and two practical examples, in which the actuators stiffness arises from Belleville washers or from an air piston, are analyzed.

Pfreundschuh, G., Kumar, V., and Sugar, T., 1991, “Design and Control of a 3 D.O.F. In-Parallel Actuated Manipulator,” Proceedings of the 1991 IEEE International Conference on Robotics and Automation .

An antagonistically actuated joint: (a) unloaded, (b) symmetric loading resulting in a possible stiffness change but no motion (assuming identical springs), and (c) an external load is applied. Note that, for clarity, the figures are aligned with the left hand end of the springs.

Belleville washer force and stiffness relationships and the net overall joint stiffness. These results are for a AM204010 Belleville washer manufactured by Rolex (38) with D=1.57″, d=0.803″, t=0.0394″, and h=0.056″. The material is steel with E=200,000 MPa and μp=0.3.

Air piston force and stiffness curves. The plots are for an Airpot® model 2K160 (bore=0.627 in. or 1.59 cm, stroke=1.5 in. or 3.81 cm). The force model results agree with data from the airpot website (39).

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